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Simplifying (3x + -0.5y + 2z) * 2 = 0 Reorder the terms for easier multiplication: 2(3x + -0.5y + 2z) = 0 (3x * 2 + -0.5y * 2 + 2z * 2) = 0 (6x + -1y + 4z) = 0 Solving 6x + -1y + 4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 6x + -1y + y + 4z = 0 + y Combine like terms: -1y + y = 0 6x + 0 + 4z = 0 + y 6x + 4z = 0 + y Remove the zero: 6x + 4z = y Add '-4z' to each side of the equation. 6x + 4z + -4z = y + -4z Combine like terms: 4z + -4z = 0 6x + 0 = y + -4z 6x = y + -4z Divide each side by '6'. x = 0.1666666667y + -0.6666666667z Simplifying x = 0.1666666667y + -0.6666666667z
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